In Δx = v₀t + ½at², both terms come out in the same unit. Which unit, and how?
Here is the car from the second kinematic equation again: it pulls away from the light at 3 m/s, accelerating at 2 m/s² for 5 s. How far does it travel in those 5 s?
First, write down the values from the question, and mark the one you want.
Next, write down the equation.
Substitute in the values, then simplify. The car covered 40 m.
A car moving at 6 m/s accelerates at a constant 2 m/s² for 3 s. What is its displacement?
Write down the values in the question:
v₀ = 6 m/s
a = 2 m/s²
t = 3 s
Write down the equation:
Δx = v₀t + ½at²
Substitute in the values:
Δx = (6)(3) + ½(2)(3)²
Simplify:
Δx = 18 + 9
Δx = 27 m
A speedboat moving at 8 m/s accelerates at a constant 4 m/s² for 3 s. Calculate the boat's displacement, in m.
A bus moving at 15 m/s brakes with a constant acceleration of −2 m/s² for 5 s. What is its displacement?
Write down the values in the question:
v₀ = 15 m/s
a = −2 m/s²
t = 5 s
Write down the equation:
Δx = v₀t + ½at²
Substitute in the values:
Δx = (15)(5) + ½(−2)(5)²
Simplify:
Δx = 75 − 25
Δx = 50 m
A cargo train moving at 10 m/s accelerates at a constant 1.5 m/s² for 4 s. Calculate the train's displacement, in m.
Back to the car at the light: it pulled away at 3 m/s, accelerating at 2 m/s² for 5 s. We already knew it reached 13 m/s — now we know it covered 40 m doing it, and no one had to measure the road.
A car moving at 18 m/s brakes with a constant acceleration of -3 m/s² for 4 s. Calculate the car's displacement, in m.
A motorcycle moving at 7 m/s accelerates at a constant 2 m/s² for 5 s. Calculate the motorcycle's displacement, in m.
A cart on a straight track moves at -4 m/s — 4 m/s in the negative direction — and accelerates at a constant -2 m/s² for 3 s. Calculate the cart's displacement, in m. Include the sign in your answer.